I know what program you're talking about. (I saw it, too, and that line confused me for a moment, too.) However, I know that Charades has been called "the game" in some circles, at some points in the past, and sometimes has been played with different rules. When she said "This isn't Charades, it's the game," she was giving him the name that she and her family use for it. If you've watched the show, you know that he comes from a different background and social class from the others at the party. I believe that this exchange was meant to emphasize that he was different. I hope that helps!